Observations were made in a tidal current off Red Wharf Bay, Anglesey, North Wales. The frictional stress at the bottom, Fb, was determined from the velocity profile within the first z m above the bottom and found to be related to the velocity at I m by a quadratic law, Fb = kpUl2, where K has the value 3-5 x 10-3. The corresponding value of the roughness length xo is 0-16cm. Current meter measurements at a number of depths between surface and bottom were made at half-hourly intervals, enabling the acceleration terms in the equations of motion to be determined. From the bottom stress and the acceleration terms, the shearing stress in the water was computed as a function of depth and as a function of time during the tidal period. While at the times of maximum current the shearing stress increased approximately linearly from surface to bottom, as in the case of steady flow in a channel, at other times the acceleration terms caused the stress to deviate considerably from a linear variation. Estimates of the vertical eddy viscosity, N,, indicated that its value was somewhat higher at middepth than nearer the surface or bottom. N , varied during the tidal period, tending to reach maximum values when the current was at a maximum and to be larger during the flood than during the ebb. The numerical values of N , were of the order of 270cm2/s during the flood and 130cm2/s during the ebb, corresponding to depth-mean currents of 35 cm/s and 39cmls respectively. The depth of water averaged 22 m. The observed distributions of velocity and shearing stress are compared with those obtained from a theoretical model, in which the eddy viscosity is taken as constant above a friction layer near the bottom.

Observations have been made of u and w , the horizontal and vertical components of turbulent velocity, in a tidal current, at heights of 50 to 175 cm above the bottom. The measuring instrument was an electromagnetic flowmeter, in which the magnetic field was produced by a. c. at 50 c/s and the p. d. induced in the flowing water was measured by two pairs of electrodes. The measuring head of the instrument was 10 cm in diameter, and two such heads were mounted on a tripod which was laid on the sea bed. The observations were made off Red Wharf Bay, Anglesey, in depths of 12 to 22 m, on a fairly flat bottom consisting mainly of firm sand. For mean currents, U , in the range 25 to 50 cm/s, the r. m. s. values of u were of the order of 10% of U , while those of w were about 6% of U . On a number of records, u and w were recorded simultaneously, and from these the Reynolds stress — ρ [ uw ] was evaluated. At 75 cm above the bottom the values of stress were from 2 to 4 dyn/cm 2 , the corresponding coefficient of correlation between u and w averaging —0·4. Auto-correlation curves and spectrum functions computed from these records showed that u contained considerably more energy in the fluctuations of longer period than w did. Other records were of traces of u or of w at two different heights and showed the smaller vertical scale of w compared with that of u . In the case of u the vertical scale appears to be only about one-third of the scale in the direction of the mean flow.

The component of turbulent velocity in the direction of the mean flow has been studied for the tidal current in the Mersey estuary. Two Doodson current meters were used, recording simultaneously on the same photographic paper. The more interesting results were obtained within about 2 m of the bottom, the two meters being supported in a stand, with various vertical and horizontal separations. The periods of the turbulent fluctuations recorded varied from a few seconds up to several minutes. Various methods of analysis have failed to show any predominant periods or bands of periods (when the effects of surface waves have been excluded), and it appears that, as in other types of turbulence, a continuous spectrum of fluctuations is present. Distancecorrelation coefficients in the vertical and lateral directions have been computed from the simultaneous recordings, as well as auto-correlation curves from the recordings of the individual meters. Inferring the distance-correlation in the direction of flow from the auto-correlations, the integral scale of the turbulence in this direction is estimated to be of the order of 7 m, compared with 14 m, the mean depth of water. From the simultaneous correlations, it is suggested, tentatively, that the scales in the vertical and lateral directions are of the same order of magnitude and of the order of one-third of the scale in the direction of the mean flow.

The frictional forces in a tidal current have been determined from simultaneous observations of the surface gradients and the currents at various depths. The observations were made a few miles from the coast, off Red Wharf Bay, Anglesey. The gradients were derived from measurements of the surface elevations obtained by a pair of open-sea tide-gauges of the Favé type, modified to give increased accuracy. The Doodson electrically recording current meter was used for the current measurements. Each set of observations extended over 24 h, and they were subjected to harmonic analysis for the semi-diurnal constituent. The data from these analyses were then used in the dynamical equations, giving the amplitudes and phases of the frictional force at the bottom, and of the internal shearing stress in the water at various depths. Five complete sets of records were obtained, three of which are considered to have given significant results. Expressing the amplitude of the frictional force at the bottom in the form F ═ kρU 2 , where U is the amplitude of the mean current from surface to bottom, and ρ is the density of the water, the results give the coefficient k an average value of 1⋅8 x 10 ─a . The internal frictional stress in the water was found to increase approximately linearly with depth from the surface to the bottom, and the corresponding values of the mean eddy viscosity have been derived.

The distribution of the semi-diurnal tidal constituent K 2 along the equator has been calculated with the aid of known harmonic constants at approximately fifty coastal stations in the northern part of the Indian Ocean. This has been achieved by use of a theorem in tidal dynamics, which connects integrals involving the tidal elevations and currents along the boundaries of an oceanic region and the equilibrium elevation over its surface. The distribution of K 2 along the equator has been obtained in the form of a Fourier cosine series. The depth of the ocean has been taken as uniform, except where corrections have been applied to the tidal data in areas where the water is very shallow. In the equatorial distribution the variations of phase give supporting evidence for recent co-tidal charts of the ocean. In addition, however, an estimate for the amplitude of the constituent is given for any point on the equator. This is believed to be the first direct arithmetical calculation of oceanic tidal distribution.